The authors examine core convergence for economies with a large finite number of agents and an infinite number of commodities. They find a serious disconnection between economies with a large finite number of agents and economies with a continuum of agents: the authors provide examples of nonconvergence of the core for large finite economies in L[superscript 1], a commodity space for which core equivalence holds for continuum economies. In addition, they show that, if preferences exhibit uniformly vanishing marginal utility of consumption at infinity, core convergence is restored.

Two of the most important refinements of the Nash equilibrium concept for extensive form games are (trembling hand) perfect equilibrium and sequential equilibrium. It is shown here that, for almost all assignments of payoffs to outcomes, the sets of sequential and perfect equilibrium strategy profiles are identical. This result is obtained by exploiting the semialgebraic nature of equilibrium correspondences, following from a deep theorem of mathematical logic.

[The core of a game, which is an abstraction of the core or set of cooperative equilibrium states of an economy, is a fundamental notion of social equilibrium. However, except for games derived from special kinds of economic situations or satisfying restrictive (balancedness) conditions, the core is usually empty. In contrast, this paper shows that, with mild and economically natural assumptions, large games always have non-empty approximate cores. The game-theoretic framework is sufficiently general to cover a wide variety of economic situations.]

The goal of this paper is to link attitude toward risk over personal consumption with attitude toward risk over social consumptions. Because many everyday choices involve risk, these attitudes enter virtually every realm of individual decision-making. We provide necessary and sufficient conditions for deducing preferences over risky social choices (which have consequences both for the Decision Maker and for others) from risky personal choices (which have consequences only for the Decision Maker) and riskless social choices, and we offer an experimental test of the theory. The experiments generate a rich dataset that enables completely non-parametric revealed preference tests of the theory at the level of the individual subject. Many subjects behave as predicted by the theory but a substantial fraction do not.

The sensitivity of Bayesian implementation to agents' beliefs about others suggests the use of more robust notions of implementation such as ex post implementation, which requires that each agent's strategy be optimal for every possible realization of the types of other agents. We show that the only deterministic social choice functions that are ex post implementable in generic mechanism design frameworks with multidimensional signals, interdependent valuations, and transferable utilities are constant functions. In other words, deterministic ex post implementation requires that the same alternative must be chosen irrespective of agents' signals. The proof shows that ex post implementability of a nontrivial deterministic social choice function implies that certain rates of information substitution coincide for all agents. This condition amounts to a system of differential equations that are not satisfied by generic valuation functions.

Many tests of asset-pricing models address only the pricing predictions, but these pricing predictions rest on portfolio choice predictions that seem obviously wrong. This paper suggests a new approach to asset pricing and portfolio choices based on unobserved heterogeneity. This approach yields the standard pricing conclusions of classical models but is consistent with very different portfolio choices. Novel econometric tests link the price and portfolio predictions and take into account the general equilibrium effects of sample-size bias. This paper works through the approach in detail for the case of the classical capital asset pricing model (CAPM), producing a model called CAPM+?. When these econometric tests are applied to data generated by large-scale laboratory asset markets that reveal both prices and portfolio choices, CAPM+?is not rejected. © The Econometric Society 2007.

This paper studies the impact of ambiguity and ambiguity aversion on equilibrium asset prices and portfolio holdings in competitive financial markets. It argues that attitudes toward ambiguity are heterogeneous across the population, just as attitudes toward risk are heterogeneous across the population, but that heterogeneity of attitudes toward ambiguity has different implications than heterogeneity of attitudes toward risk. In pa rticular, when some state probabilities are not known, agents who are sufficiently ambiguity averse find open sets of prices for which they refuse to hold an ambiguous portfolio. This suggests a different cross section of portfolio choices, a wider range of state price/probability ratios, and different rankings of state price/probability ratios than would be predicted if state probabilities were known. Experiments confirm all of these suggestions. Our findings contradict the claim that investors who have cognitive biases do not affect prices because they are inframarginal: ambiguity-averse investors have an indirect effect on prices because they change the per capita amount of risk that is to be shared among the marginal investors. Our experimental data also suggest a positive correlation between risk aversion and ambiguity aversion that might explain the “value effect” in historical data.

This paper offers a new approach to the study of economic problems usually modeled as games of incomplete information with discontinuous payoffs. Typically, the discontinuities arise from indeterminacies (ties) in the underlying problem. The point of view taken here is that the tie-breaking rules that resolve these indeterminacies should be viewed as part of the solution rather than part of the description of the model. A solution is therefore a tie-breaking rule together with strategies satisfying the usual best-response criterion. When information is incomplete, solutions need not exist; that is, there may be no tie-breaking rule that is compatible with the existence of strategy profiles satisfying the usual best-response criteria. It is shown that the introduction of incentive compatible communication (cheap talk) restores existence. Copyright The Econometric Society 2002.